ABSTRACT
Problem 1. Solve the equation x2 + x − 6 = 0 by factorization
The factors of x2 are x and x . These are placed in brackets: (x )(x ) The factors of −6 are +6 and −1, or −6 and +1, or +3 and −2, or −3 and +2. The only combination to give a middle term of +x is +3 and −2, i.e. x2 +x − 6 = (x+ 3)(x − 2) The quadratic equation x2 + x − 6 = 0 thus becomes
(x + 3)(x − 2) = 0 Since the only way that this can be true is for either the first or the second or both factors to be zero, then
either (x + 3) = 0, i.e. x = −3 or (x − 2) = 0, i.e. x = 2 Hence, the roots of x2 +x − 6 = 0 are x = −3 and x = 2.
